Various types of sheet gripper arrangements are known and in general use in rotary printing machines in order to transfer sheets from one drum or cylinder to another. One such gripper system is described in the "M.A.N. Printing Machinery News", vol. 51, page 28. This system, similar to other systems, as customary, has gripper fingers coupled to a gripper spindle, cooperating with gripper surfaces which are positioned on a gripper rail, part of or carried on the drum to which the gripper is attached. As customary, the gripper spindle is journaled at the axial ends in spindle carriers which are rigidly secured to the cylinder shaft. Positioning rings are located adjacent the carriers, usually at the outer axial ends, to position the gripper spindle, without play, in axial alignment. The grippers, and hence the gripper spindle, must be properly aligned so that no differences in register will occur upon printing. Lateral deflection or deviation of the gripper spindle in axial direction with respect to the associated cylinder of the printing machine, may cause doubling or register misalignment, and axially fixing the gripper spindle is thus required. It has been found that grippers in printing machines operating at high speed, and hence transporting printed substrates at high speeds have different holding forces in different ranges of the gripper spindle. The holding forces between the gripper fingers and the matching gripper pads or rails can vary so much that the substrate may be pulled out from the grippers, or misalignment may result. Some zones across the printed sheet which are gripped, thus, may have lesser gripper force than others. In a worst case situation, the substrate may separate entirely from the grippers.